An inverted pendulum is a classic case of robust controller design. A successfully validated and precise system model would greatly enhance the performance of the controller making system identification as a major procedure in control system design. Several techniques exist in literature for system identification, and these include time domain approach and frequency domain approach. This paper gives an in-depth analysis of system identification and modelling of rotary inverted pendulum that describes the dynamic models in upright and downward position. An extensive elaboration on derivation of the mathematical model describing the physical dynamic model of the rotary inverted pendulum is described in this paper. In addition, a frequency response function (FRF) of the physical system is measured. The parametric model estimated using non-linear least square frequency domain identification approach based on the measured FRF is then applied as a mean to validate the derived mathematical model. It is concluded that based on the validation, the dynamic model and the parametric model are well fitted to the FRF measurement.

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